Ropes designed as personal protective equipment are normally low stretch or high stretch. If a line is marketed as static, it is normally pre-stretched or made of a high modulus fibre such as Aramid.
The European standards for rope designed as a lifeline must meet the following:
EN 1891 - low stretch kernmantel ropes
Type A & B.
EN 892 - Dynamic mountaineering ropes.
Ropes used for work positioning (ie tree work)must comply with EN 1891 Type A.
If fall arrest is a possibility, a dynamic rope is not considered sufficient to absorb potential forces, so an energy absorber and full body harness should be worn. EN 892 is for sport use.
Because of the stringent testing involved with these standards, the EN numbers could be taken as a mark of quality. I would never recommend using a static line for working in a tree except for access with a bomb proof anchor.Always make sure that the line meets or exceeds national standards for life support, not just some piece of chandlery.
Tree ropes (single braids) are not classic kernmantle ropes but could be classed as such - just that the outer jacket has a mass of 80% with associated strength. However, Arb lines sold in the EU are still tested under EN 1891 Type A and routinely pass.